Filtering network



Sept. 30, 1958 P. DAGUIER 2,854,641

FILTERING NETWORK Filed Maron 15, 1955 l s sheets-sheet 1 (La) -wo/a Sept. 30, 1958 P. DAGUu-:R 2,854,641

l 5 FILTERING NETWORK Filed March 15, 1955 3 Sheets-Sheet 2 #g2 Eg. 3

pti/ay 2 E61/ay L/nef me/ 2 L 3 -M/'xer y n 3 T-/V/'xer j S Delay Lime'- 2 Sept. 30, 1958 P. DAGUIER FILTERING NETWORK Filed March 15, 1955 3 Sheets-Sheet 3 (/Q-ce/l (Band-,nasi

/me ffffef 11A/VENTO?? nib - ff' 2,854,641 Ice Patented Sept. 30, 1958 It is an other object of the invention to provide means whereby a ltering network of transfer characteristic G w sin a w-wo FILTERING NETWORK 5 t --L(w w0) Plel'le Dagllel', La Coflmellve, France, assignol' t0 Societe may be obtained by combination of lumped or distributed Nouvelle de lOutillage R. B. V. et de La Radloimpedances- Indusme Pans France lt is another object of the invention to provide means Application March 15s 1955, serial Nm 494,341 for the realization of a circuit, the transfer function is of the type Claims priority, application France March 19, 1954 11 Claims. (Cl. S33-70) comprising a limited number of circuit elements. 15 It is another object of the invention to provide means The invention relates to the realization of ltering netof reahzatlon of a lter of transfer characteristic works of transfer characteristic ofthe type G(w) such that A sin a(w-w0) G(w):A sin a(wwo) i (l) v G(w): ouv-wn) "wwol in which where A and a are parameters independent of the fre ,w quency fo of the incoming signal fo: 2 0 v 'Il' [ftg may take any particular value including zero.

lr According to the invention, the filter of transfer charassuming that fo may take any value including zero. The acteristic use of such filtering networks is very wide. Indeed, they p A sin a(w w can be used each time that it is necessary to develop a G(w):ww-

transfer characteristic of the type G(w) since they may operate in a very wide band of frequencies from video COInPIiSeS e limited number of elementary Cells aSSO- frequencies (f0=0) up t0 ultra-high frequencies and ciated with a pass-band lter, each cell comprising a delay hyper-frequencies as will appear 131er on, This wave .i line and a direct connection in parallel, the delays introshaping may be requiredeither at the transmitting end or dneed by the different eellS being Chosen S0 2S t0 C011- at the receiving end of a transmission channel. Con- Stinte a geometrie Series Ofdeoernent 1/2- The lafgeSt sidering the use of such circuits at the receiving end, delay introduced by any one of the Celle constituting the some results of the infor-mation theory should he recalled lter is equal to a parameter a and should be equal to to point out the advantages which are provided by the a multiple of half the period of the carrier wave of use of circuits according to the invention in detecting frequency fo provided such a carrier wave exist-s.

incoming pulses which are mixed up with noise signals. According to an embodiment of the inVention, en Indeed, it is well known that the best conditions to detect amplifier stage is provided between successive cells. such signals when the noise is supposed to show a random According to another embodiment of the invention,

distribution in all the frequency spectrum, is to use a the coupling element between cells comprises an additive receiver the gain or transfer characteristic of which is constage which provides the direct connection and which'is jugated with the information through a Fourier transconnected in parallel with the delay line. formation. FunctionfG(w) may be shown to be the In another embodiment of the invention, amplification Fourier transformation of a sinusoidal oscillation at `may be provided at the output of each cell Vor of some frequency fo which is modulated by a rectangular pulse of the cells or at the end of the ltering network.

of duration 2a. Since this function is real, it is its own According to another feature of the invention, the conjugate. This shows that the filers according to the band-pass lilter associated to the cells may be constituted invention are the best circuits to detect recurrent pulses by several elementary band-pass lters connected sepawhich are received together with a randomly distributed rately to individual cells and showing diiferent characternoise signal. Such a problem has a very large technical i istics versus frequency. It may also be included in the application since` it corresponds to the problem of recepsource of input signals when such a source comprises a tion in most of the pulse type telecommunications at lixed pulse receiver the passeband characteristic of which is of carrier frequency, and also to all the pulse detecting syscourse limited. tems such as radar. As is well known from the thory, the transfer char- The deSCriptiOn Which follOWS iS nialnly dileeted to the acteristic of the filtering network is the product of the use and embodiment of the filter according to the intransfer characteristic of each of its constitutive cells. vention when applied to the reception of pulses. How- Such a product is of the algebraic type and therefore, it

eVeI, this Choice of one Particular tYPe of utlliSation of is possible to change the order of succession of the difterhe ltelS according to the inVentlon Should Ilot be Conent cel-ls which constitute the lter from the normal se- Sidered a'S a limitationl of its SCoPe of dPPlifatiOn In' quential order of terms of the series of decrement l. deed, the lltel" aooodlng to the Invention 1S also Vef'y This is also the reason why it is possible to constitute the Useful When 11Sed to operate on Video slgndlS, thatds pass-band ilter associated with the elementary cells as .rectangular PUlSeS Whloh do .nota Inodi-date any Carrier several elementary lters where such a possibility is prewave. Such ilters may be used lndeed as aperture corferred from the technical peint of view,

Teotlng 1l'ledilsfin Pulse transmitters o1- receivers To fully understand the operation of the lter accord- It iS therefore an ohleot of the invention to Provide e ing to the invention, it is necessary to recall some well filtering network the transfer characteristic of which is known mathematical results Curves A and B of Figure 1 0f the type y 70 show, respectively, a rectangular impulse as a voltage amplitude versus time and the Fourier transformation of A sin G(w-wo) such a signal as amplitude versus frequency f or pulsatlon w (with w=21rf). vThe mathematical expression'of mwhere UU) is Heavisides impulse function, 2n is the pulse duration and wo the pulsation of the carrier wave of frequency fo. The `Fourier transformation of function A(t) is given by G(w) with When. n becomes iniinite the product of Equation 4 is :convergent and therefore, litis possible to write If equation 5 is limited to a finite number of terms, the

r limited produce: gn(.w:) .is no longer identical to G(w).

However, in a limited range of Variations ofthe 'variable (w*w0) around wo, gn (w) is all the more near to G(w) that the numberiof terms ofthe product ofl cosinus -is greater. Accordingly, if n terms are considered', n being finite, the limited product -may be takenfinstead of G(w) in affrequency band around The right end part of Equation 6 is a periodic function of w, theiperiod being l l a X21z Ihis function is an even function of (w-wo). Curve C of Figure 1 is representative of function g3 (w) such as g3(w) :2 cos (w-wo)a/2.cos

(w-w)a/4.cos (w-wOM/S (7) Around w=w0, curve C is Very near curve B. The periodicity of curve C is and the frequency interval between a maximum and the adjacent minimum is 4 if-z Figure 2 is a schematic diagram of an elementary cell constituting the filter according to the invention. E shows the input of the cell. Lead 1 shows the direct coupling between input E and the additive circuit 3 which feeds output S. 2 is the elementary delay line. The filtering network is supposed to comprise n such elementary cells. The delays introduced by successive elementary delay lines such as 2, constitute a geometrical decreasing series of decrement 1/2 the longest delay being equal to a. The output signal developed at the end feeds a band-pass filter tuned at frequency fo or a harmonic of fo. As will be understood, this filter may be constituted by another elementary cell of the type shown on Figure 2, the elementary delay line 2 of which introduces a delay 4 where p-1 n if a Ta n' isv they shortest delay of any cell of the network.

Figure 3 shows a filter incorporating three elementary cells. The output band-pass filter is shown at 4.

It is easy to show that the transfer characteristics of the circuit made of a set of elementary cells such as shown on Figure 2 is of the form g(w) which has been referred to above. Let,A(vt) be the input signal applied at E of the elementary cell of Figure 2. The output signal from delay line 2 may be written as AFAcMm/W" (s) The output signal from the elementary cell is given by S2=Ae (1+ef'w/2) 9) f =A(t)(l+cos a/Z'If-l-i-j sin a/2"1) (10) The transfer characteristic of the elementary cell is thereby given by tgzlrlcos wtf/2"m1 The transfer characteristic of a set of three elementary stages such as shown on Figure 3 is given by f since the successive delays introduced by the elementary delay lines constitute a geometrical series of decrement 1/2. When the input signal A(t) is a rectangular pulse such as shownvby curve A of Figure 1 and if the carrier 1 K2" fo: a

corresponds to values of wo such that the terms in cosinus of the equation sin (tu-wohl (w-w0)a are simultaneously equal to +1 or -1. Therefore, at frequency fo of the carrier wave, each one of the terms of the product must be either minimum or maximum. This condition may be written by reference to Equation 14:

In other words, the carrier frequency should be a multiple of the reciprocal of the longest delay (a) intro duced by one of the` elementary cells of the filter network. It is easy to fulfill this condition, supposing a known, by heterodyning the input signal with a local oscillator of correct frequency, When the filter is such as shown on Figure 3, that is when the filter comprises three elementary cells, the transfer characteristic of the circuit-is-Equation y 14. *The filter is connected to a band pass filter 4 which transmits only the youtput signal frequencies which surround frequency fo or another maximum or minimum of curve-C `ofFigure 1. The dashed line on curve C shown by reference 4 corresponds to the band-pass characteristic of output filter 4 of Figure 3.

- VIt'r'nay be seen that each time, another elementary cell isl addedto the lter, another co'sinusl term is added to the transfer characteristic equation. In other words, the frequency interval df between two successive maximums of the representative curve of the transfer function g(w) is multiplied by 2. This remark will help in designing fi1ter'4.- It is also easy toshow that the output energy transmittedA through pass-band filter r4r is increased approximatively by the same factor 2. Therefore, it is possible to 'decide how many cells willv be used to obtain a given energy' at the output ofthe lilter.V

Figures 4, 5 and 6 show detailed wiring diagrams of embodiments ofthe invention designed for reception of pulsesythe duration'of which (2a)`is equal to 1 its. at a carrier frequency f1, of 16 mcs. These numerical values have been 'chosen `because 'they correspond to actual realizations but do Anot constitute any limitation to the scope of application of the lters according to the invention. Of course, owing'to the fact that the total delay of the elementary cells is at most equal to the pulse duration, the input signal which may be applied to the circuits according to the invention should have a recurrent'periodicity smaller than the pulse duration.

The reference numbers on Figure 4 are the same as the one used onFigures 2 and 3. The delay line introduces a delay a=0.5 fis. Y,

In a particular embodiment of the invention the line is made ofan-artiicial line comprising 40 identical cells .eachmade of a coil of inductance L=4.9 fil-I. and a condenser ofcapacityv CLV-25 (pF.r The mutual inductance betweenA two adjacent coils is approximatively 0.09 MH.

The total inductance of the line is 250 pH.; the characteristie impedance is equal in value to the resistance of terminal resistors R that approximates 530 ohms. The

complete delay line of forty cells is-placed on an insulating plate of 30 centimeter length. As shown, the delayed signal delivered bythe line is applied to the control grid of tube V1. The'input signal is transmitted, through attenuator 11 ywhichprovides the same attenuation as the delay line so that the peak levels of both signals should be equal, tothe control grid of a second tube V2. Addition 'of these ltwo signals is obtained by connecting the plates of tubes V1 and V2 in parallel. The output signal is applied by means of coupling condenser vC1 of high capacity to the 'followingstage of the filter shown at 12. This stage is designed in the same way as the stage which has just been described with the diterence that the delay line comprises .only 20 identical. cells. In the same way, stage 13 of the filter includes a delay line comprising-l 'identical cells which introduce a delay equal to 1A; ps." The outputfrom. stage 13 isv fed to pass-band filter 4. The latter may be reduced to a circuit tuned at frequency ;f0, the transmission characteristic of which is as shown on curve C of Figure 1 at 4.

In another embodiment of the invention, a modification of Figure 4 shown in the block diagram of Figure 4a, the output from attenuator 11 of each stage is applied directly to the input of the delay line of the following stage which modification omits tube V2, the addition being provided directly by connecting in parallel the direct lead 1 and the delay line terminal'.

Figure shows another embodiment of the invention in which the input signal is applied to the control grid of a rst amplier stage V5 comprising a resistive load R. The delay line shown as an artificial line of surge impedance R is connected in parallel with load resistor R. The end of the line is opened (that is the line is terminated on condenser of the last cell) so that the signal will be reflected Yat the end of the line. Therefore, the delay introduced corresponds to therduration of the propagation of the signal in both directions along the line. This delay is equal to 0.5 ps. The line comprises-for instance 20 cells identical with the one just described and therefore requires a volume half of the volume occupied by the delay line of the first stage of the embodiment shown of Figure 4. The output signal from V5 is applied to the control' grid of amplilier V5 which feeds the second stage and so on. Coupling is performed by condenser 15 of high capacity with respect to the condensers of the artificial line. It is easy to show that the input impedance of the delay line associated to stage V5 is given by #J'R Ze-tgwa/2 Where R is the characteristic impedance of the line. The load impedance of tube V5 comprises the parallel network made of a resistor :R and the delay line. It is easy to calculate the modulus yof the load impedance Z and the exponent respectively- The embodiment shown on Figure 6 requires the use of a greater numberv of tubes but allows amplification between two successive stages of the iilter, together with automatic compensation of the losses in the delay lines. In this embodiment, coupling between stages is provided by means of cathode follower stages which provides a stable operation of the filter relatively to Variations of the internal resistance of the coupling stages either due to ageing or to the -tube manufacturing. vInput signal is applied to the control grid of amplifier stage V5, the load impedance of which comprises resistor R connected in parallel with the delay line of characteristic resistance R, closed on an adapted resistor. The delay introduced by the line is 0.5 ps. The signal across load resistor R is appliedv to the control grid `of a first cathode follower stage V10. The output Vsignal delayed by the line is applied to the control grid of a second cathode follower stage V11. The output circuits of V11 and V10 `are connected in series by means of balancing resistors R1 and R2. A potentiometer P is used to pick-up the correct fraction of the output signal which is 'the sum of output signals from V10 and V11. The use of two resistors R1 and R2 of different values and the control of the gain of stages V10 and V11 enables to compensate, in each stage, the losses occurring in the delay line. The use of tubes V10 and V11 provides a better adaptation of the delay line and prevents multiple reflections of the pulses at the end of the line.

The embodiment shown on Figure 5 provides an economy on the required number of tubes and may be advantageously used when the delays a, a/Z, etc., are suliiciently small so that the losses in the delay lines are negligible. The embodiment shown `on Figure 6 is'preferred when this condition is not fulfilled.

The realization of the delay line of the different stages depends on the frequency of operation. At ultra high frequency these lines should comprise either a certain length of transmission line or sorne kind of cavity; at microwave frequencies the delay is provided by a length of wave guide.

When the incoming signal is constituted by video signals, that is rectangular pulses without carrier wave, the iilter according 'to the invention may be used and will operate in the same way. The delay line should be designed to operate at video frequencies and the pass-band ,filter 4 is replaced by a low-pass output lter.

As was said above, the use of the filter according to the invention is by no way limitated to pulse reception. For instance, if very short pulses are sent in the iilter according to the invention, the output signal from the irst stage (see Figure 2) will comprise two short pulses separated by which is the shortest delay introduced by any of the stages constituting the filter, is very small with respect to the pulse duration of the input signal. The output from the second stage will be a set of four short pulses occurring at time intervals of and so on from stage to stage. After the nth cell, the output signal is a set of 2n pulses which are regularly occuring at time intervals and which occupied a time duration equal to The envelope of this set of pulses is a pulse of the same duration. This pulse is composed of `a iinite series of sinusoidal waves, the frequency of which are successive harmonics and which are set by the delay introduced by the successive stages of the iilter. The phasing of these sinusoidal waves only is determ-inated 4by the leading edge of the input signal.

What I claim is:

l. A lilter network of transfer characteristic A sin ami-wo) ctw-wo) where A and a are parameters independent from the frequency wo is a constant parameter which may take any value such as with n being an integer 20, said ilter network comprising a plurality of elementary networks connected in cascade, each elementary network comprising a direct transmission` channel and a delayed transmission channel connected in parallel between an input terminal and an output terminal, transmission delaying means included in the transmission delay channels of successive elementary networks to introduce in successive elementary networks decreasing amounts of delay according to a geometric series of lirst term (a) and a decrement of 1/2.

2. A iilter network according to claim 1 and including a band-pass iilter connected in said cascade and having a 8 middle frequency fo related to the maximum delay (a) in accordance with i i i c i where n is an integer 0.

3. A r,filter network according to claim 1 and including attenuating means in the direct transmission channels of said elementary networks. i

4. A filter network according `to claim 1 and including amplifying means inserted between successive elementary networks.

5. A filter network according to claim 2 wherein said band-pass iilter compriseselementary filters embodied in said elementary networks.

6L A filter network accordingto claim 2 in which said band-pass filter is included atleast in part in an input signal source feeding said iilter network.

7. A filter network according to 'claim 1 in which each elementary network'includes balancing means for con,- necting the two channels to the output terminal.

8. A iilter network of transfer characteristic weer# said lter network comprising a plurality of elementary networks connected in cascade, each elementary network comprising a direct transmission channel and a delayed transmission channel connected in parallel to an input terminal and an additive stage connecting said two channels to a common output terminal, output terminal, transmission delaying means included in the transmission delay channels of successive elementary networks to introduce in successive elementary networks decreasing amounts of delay according to iageometric series of first term (s) and a decrement of 1/2.

9. A iilter network accordingto claim 8 and including a low-pass lter connected in said cascade.

10. A lter network according to claim 8 and including attenuating means indirect transmission channels of said elementary networks.

11. A iilter network according to claim 8 in which said low-pass filter comprises elementary lters embodied in said elementary networks.

References Cited in the ijle of this` patent UNITED STATES PATENTS 1,926,097 Hansell Sept. 12, 1933 2,024,900 Wiener et al. Dec. 17, 1935 2,124,599 Wiener etal July 26, 1938 2,629,841 Peterson Feb. 2.4, 1953 UNITED STATES PATENT OFFICE Certiicate of Correction Patent No. 2,854,641 September 30, 1958 Pierre Daguer It is hereby eerted that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

1n the grant, line 1, name of inventor, for Pierre Dagner read Pier/re Dagwie'r; n the printed speeeation, column 4,1ine 18, for that portlon of Equation (9)'read'mg 152: read S1= column 7, lines 18 and 19, for the mathematical expression Signed andsealed this 24th day of February 1959.

[SEAL] Attest: KARL H. AXLINE, Attesting Oyicer.

ROBERT c. WATSON', Uommissione? of Patents.

UNITED STATES PATENT OFFICE Certiicate of Correction Patent No. 2,854,641 September 30, 1958 Pierre Daguer It is hereby eerted that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

1n the grant, line 1, name of inventor, for Pierre Dagner read Pier/re Dagwie'r; n the printed speeeation, column 4,1ine 18, for that portlon of Equation (9)'read'mg 152: read S1= column 7, lines 18 and 19, for the mathematical expression Signed andsealed this 24th day of February 1959.

[SEAL] Attest: KARL H. AXLINE, Attesting Oyicer.

ROBERT c. WATSON', Uommissione? of Patents.

UNITED STATES PATENT OFFICE Certificate of Correction Patent No. 2,854,641 September 30, 1958 Pierre Daguier It is hereby certified that error appears in the above numbered patent reqlrng correction and that the said Letters Patent should read as corrected below.

In the grant, line 1, name of inventor, for Pierre Dagiiiei' read Pierre Daguzer; in the printed specification, column 4:, line 18, for that portion of Equation (9)'reading 82: read S1=g column 7, lines 18 and 19, for the mathematical expression 2 read a al 2 Signed and 'sealed this 24th day of February 1959.

Attest: KARL H. AXLINE, ROBERT C. WATSON, Attesting Ocer. Commissioner of Patents. 

